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Friday, 16 January 2015

How to Get Rich - The Beauty of Compounding to Investors and Companies

"Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it." - Albert Einstein.

I’m always
amazed by the mechanics and impact of the compounding effect. The basic compound
interest formula is:-

Where:

F = Future value or final value of the
investment
P = Principal or the starting capital
r = Annual rate of return
t = The number of years this return is compounded

To let the compounding effect work its
wonder, an investor needs to focus on the Starting Capital (denoted by P),
Annual rate of return (r) and the number of years (t). Let’s use $100,000
starting capital, 10% annual return and 20 years as baseline inputs for
comparisons with other permutations. For simplicity, effects of inflation are
neglected throughout.

Effects of Compounding with Various Inputs

As observed from the table and chart, for all cases the
value of gains is much more than the initial capital itself. But what can we really
learn from these results and what can we do to maximize the compounding effect?

I find it quite worthwhile to classify these inputs based on
the level of control we have over them. By identifying them singularly, we can
find out which inputs we are lacking and categorically work on them.

Time Factor (t)

As observed above, time is an absolute critical factor for
the effects of compounding to snowball the initial capital as much as possible.
All of the input invested 7 years late did worse than the baseline input. If we
have $100K and can compound 10% for 20 years but we do it 7 years later, our
gains is a 57% or $327K lesser! 7 years later is 7 years too late. This is
something that we can control only when
we are still young. The key is to start investing as early as possible and have the patience to let the compounding effect work.

To put it into practical perspective, if a 40 year old who
earns an average of $100K per year invest with baseline results, he will have
an extra $245K by 53 years old. This would mean that his investments gave him
an extra 2.45 years of working income. However, if he started 7 years earlier
at 33 years old, he will have an extra $570K by 53 years old which also means
that he gets an extra 5.7 years of his working income. Why work another 5.7 years
when you can actually get the same amount of money with less effort? Retiring a
few years earlier is certainly not bad at all!

Starting Capital (P)

The Starting Capital is also important but comparatively less
controllable. Different individual profiles will have differing amounts of starting capital to
invest. Most of the time, we can’t really control how much we have at the start (especially when we are young). However, all of
us have universal control in terms of the proportion
of our money we set aside to save and invest. This is a definitely a decision that
can be made and acted upon for almost everyone.

Return Factor (r)

Can we really achieve 10% returns per annum for our
investments? No one knows. Sometimes its luck and other times it may be because of innate talent. I believe the best way to potentially improve anyone’s returns is
through continually seeking and acquiring investment & financial knowledge.
This is definitely something within our control. There are many books, articles
and videos online and offline that teach us how to make our money work harder
for us. Of course, this takes time and effort but I think it’s the only way to handle
this factor properly.

The Real Trick –
Combining All 3 Inputs

What’s the use if we can earn an impressive return from our
investments but we can compound it for only 2 years? There’s also little use
when we have 30 years to compound our money when we can only achieve a 2%
return. The real trick lies in combining all 3 inputs in the compound interest
equation. To do this, we first need to tackle each factor separately by (a) Identifying
which factor we are lacking the most, (b) Find out what we can do that is within our control to improve the factor, (c) Work on improving them and (d) Repeat the process again starting from part (a).
Let me know if you have other ways to optimize the compounding magic :-)

Note: Just want to highlight that there’s
another factor that is not included in this simple compound interest equation.
That is the additional cashflows you can add into your investment sum every
period. Imagine you can compound 10% in 20 years with a starting capital of
$100K and on top of that, you are also able to contribute another $12K into your
portfolio annually - Your final value would be $1.36M with a contribution of
$340K in total. This is compared to the baseline case mentioned above with
$672K final value and $100K contribution.

This post
is longer than expected. I’ll talk more about the companies which can continually compound their value through time from an investor's viewpoint.

I think you’ve posed a very valid case here about finding out which is the most important factor. Honestly, I'm not very good at such simulations. But if you've noticed, I've used a factor of 1.5 for rate of return, r and starting capital, P in the case study (i.e $100K x 1.5 = $150K, 10% x 1.5 = 15%). For time period, t, if we use a starting capital of $100K and 30 years (20years x 1.5), the final amount would be about S$1.75M. From this single but likely inconclusive datapoint, it appears that time period and rate of return are the most important factors to consider.

Unfortunately the rate of return probably is one of the least predictable of the 3 factors since there's no way we can be sure we can achieve 10% or 15% return over the long haul. Because of this unpredictability, I thought it is not so useful to state which factor is the most important in the practical sense. However, very fortunately for us, the time period is quite within our control and easily ‘applied’ if and only if we are young enough to start. Then again, achieving a 2-3% return over the long haul is probably easier than say, compounding it for 50 years due to the limitations of being a human. A balanced effort in working on all factors should be the better way to handle the compound equation.

All the 3 factors are highly intertwined and complementary to one another. For example, compounding $100K at 15% for 18, 19 and 20 years will give $1.24M, $1.42M ($180K more from 18th year), $1.64M ($220K more from 19th year) respectively. A good compound rate is important but the effect will be more pronounced if the length of time is extended due to the exponential effect of the formula. Similar relation applies for the other factors.

In conclusion, due to the varying ease of application and unpredictable nature of some factors, it is quite hard to conclude decisively which factor will do most for us in our lifetime. Consequently, I believe the best way to reconcile this is to focus on all 3 factors based on my proposed method to tackle each factor in my post (under The Real Trick – Combining all 3 Inputs).

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